To determine the sum of the measures of the interior angles of a dodecagon (a polygon with 12 sides), we can use the formula for the sum of interior angles of an n-sided polygon, which is:
[tex]\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\][/tex]
Here, [tex]\(n\)[/tex] represents the number of sides of the polygon.
For a dodecagon, [tex]\(n = 12\)[/tex]. Substituting this value into the formula, we get:
[tex]\[
\text{Sum of interior angles} = (12 - 2) \times 180^\circ = 10 \times 180^\circ
\][/tex]
Now, multiplying:
[tex]\[
10 \times 180^\circ = 1800^\circ
\][/tex]
Therefore, the sum of the measures of the interior angles of a dodecagon is [tex]\(1800^\circ\)[/tex].
The correct answer is:
[tex]\[
\boxed{1800^\circ}
\][/tex]
